Task 7 (Sobolev spaces) Prove the weak main theorem of differential calculation 2), 3).
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- Double integrate under z=xy, above the triangle with vertices (0,1),(0,4),(1,1).Find the work done by the force field 2 2, , , 3 , x y z z z y z z x F in moving a particle along the line segment from (0, 2, 0) to (−4, 3, 2).What is the relationship between the curvature tensor and the Riemann curvature tensor in differential geometry?
- 3 I want to convert z=x2−2xy+1 to tensor product blossom and compute the control points if its over square[0,1]^2. Could you guide me how or give me a hint please?resolver usando la transformada de Laplace y"+6y'+5y=t-tU(t-2), y(0)=1, y'(0)=0Define a new interpretation of the description “dynamical system” for a collection of interdependent differential equations?
- Show all work of integrating x and y. As specificWhat is the Divergence Theorem? Explain how it generalizes Green’s Theorem to three dimensions.A particle starts at the point (−4, 0), moves along the x-axis to (4, 0), and then along the semicircle y = 16 − x2 to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = 5x, x3 + 3xy2 .